One family of finite elements that is often used for velocity or momentum variables is the Raviart-Thomas family, which can be defined on triangular or quadrilateral cells.
The previous decade has seen particular interest in these finite elements from the numerical weather prediction (NWP) community.
In many of the finite difference or finite volume methods used historically by this community, the density/pressure and velocity variables have been staggered according to the Arakawa C-grid of [1]}, [2]}, [3]},
due to its good representation of the wave modes of the shallow-water equations [4]}.
It was shown by [5]} that certain choices of finite element pairs for the density/pressure and velocity variables can still replicate the desirable dispersion properties of the Arakawa C-grid in a mixed finite element model of the shallow-water equations.
In particular, the finite element equivalent of the velocity staggering used in the Arakawa C-grid on quadrilateral cells is the lowest-order Raviart-Thomas elements (i.e. the elements using the lowest degree polynomials in the basis functions).
Maintaining this equivalence by using the lowest-order finite element spaces can be advantageous for other reasons, for instance that it can simplify the coupling to parametrisations which are used to represent unresolved physical processes in NWP models.
